Suggested benchmarks for shape optimization for minimum stress concentration

Shape optimization for minimum stress concentration is vital, important, and difficult. New formulations and numerical procedures imply the need for good benchmarks. The available analytical shape solutions rely on assumptions that are seldom satisfied, so here, we suggest alternative benchmarks. The existence of singularities forces us to separate the design modeling (parameterization) from the analysis modeling, which from a practical point of view, is finite element (FE) modeling. Furthermore, the obtained stress concentrations depend highly on the FE modeling and cannot be used as a primary benchmark value. In the present study, we choose to work with shape description by a few parameters and the obtained benchmark shapes are exactly specified to facilitate alternative analysis procedures for comparison with differently obtained shapes. In this manner, the dependence on the specific analysis procedure is avoided. As examples, we use a sensitive stress concentration problem for fillets or cavities in tension (or compression). These problems are solved as three dimensional (axisymmetric) and as plane stress and plane strain cases. Further cases with design of shapes for a T-head fillet are also presented in this parametric study.